Methods such as beam deflection, astigmatic detection, and capacitance measurement are commonly used for micrometer scale and nanometer scale measurements of the position and orientation of a target object. These precision displacement measurement systems are sensitive to environmental changes, such as changes in temperature or humidity or changes to internal components of the system. For instance, beam deflection and astigmatic detection use optical measurement schemes involving a light source (e.g., a laser), lenses, and a photosensor. A change in ambient temperature or humidity may cause a change in the wavelength emitted by the light source. Thermal gradients caused by heat sources (such as the light source) within the displacement system and/or stress relaxation in components of the system can affect the separation between different components inside the displacement system, resulting in drift of the detection signals. A change in ambient temperature or humidity affects signals in the electronic circuits, such as circuitry in a displacement sensor of the system. Furthermore, the heat capacity of the instrument can cause a time delay of temperature-related drift. In general, the more components there are in a displacement measurement system, the more susceptible the system becomes to both internal and external environmental changes.
Thermal expansion is a main factor influencing signal drift. Even if a displacement sensor is fixed by firm mechanical attachment, the detected displacement signal representative of the spacing between the sensor and a target object may still drift with time due to a slow change in the spacing. For instance, aluminum is widely used in manufacturing the frame of many instruments because it is relatively inexpensive and easy to machine. Aluminum has a thermal expansion coefficient of 22.2×10−6 m·K−1. This means that if two components are fixed on an aluminum frame separated by a distance of 10 mm, a one degree increase in temperature will cause a 222 nm increase in spacing between the two components as a result of thermal expansion of the frame. Under the same conditions but using steel instead of aluminum for the frame, the increase in spacing would be 130 nm. Furthermore, each component in a precision displacement measurement system may have a different thermal expansion rate, and thus it is not always straightforward to predict the magnitude and the direction of drift in a displacement measurement. For a displacement measurement system with nanometer resolution, thermal drift of hundreds of nanometers seriously degrades the measurement precision and accuracy.
In many displacement measurement systems, the surface of a sample is positioned within a certain distance or angular range of the displacement sensor. For instance, an astigmatic detection system (ADS) measures translational displacement of a sample along one axis and angular displacement of the sample around two axes. The ADS includes an optical path mechanism in which a laser beam is focused on the surface of an object by a lens assembly. Light reflected from the object surface passes back through the lens assembly and forms a light spot on a photo sensor. The shape and position of the light spot on the photo sensor are used to determine translational and angular displacements of the object. The ADS is capable of detecting displacements of the object when the object surface is near the focal point of the detection light beam and/or within the linear region of the focus error signal of the ADS. The typical linear range of the focus error signal is about 6-8 μm. To adjust the height of the object surface to be within the linear region of the ADS, a fine linear translation stage may be used. However, even with a fine adjustment stage, signal drift problems still arise and can cause the object surface to drift out of the detection region of the ADS displacement sensor.
There are several strategies for minimizing or avoiding signal drift of a micrometer-scale or nanometer-scale displacement measurement system. The use of materials with a low thermal expansion coefficient, such as granite (3.7×10−6 m·K−1), Invar® (1.3×10−6 m·K−1), or Zerodur® (0.02×10−6 m·K−1), reduces thermal expansion of the instrument, but such materials are expensive and difficult to machine. Alternatively, the environment of the displacement measurement can be carefully controlled by air conditioning or other ambient control systems. However, such systems can maintain the temperature and humidity only within a certain range. Further, actuators and sensors in the displacement measurement system are parasitic heat sources that create local time-varying temperature gradients that are not easily mitigated by room-level ambient control.